There are plenty of reasons why mail wouldn't reach a give email address.

One of the most common cause of failed mail delivery is due to a given account being overquota. Have you considered this?

To check what is happening, try sending an email to the given email address and then observe the contents of /var/log/exim_mainlog as any error, if the mail is reaching the server, will be recorded here.

Consider also whether the MX record for the domain in question is working correctly. Does it point to the correct IP address, does the IP respond? How busy is the server? Is it overloaded to the extent where received mail is taking a long long long time to process?

Do you have any forwaders or filters in place that could be affecting where mail is delivered? Consider removing them to see what difference this may make.

Lastly, if you're not the server administrator, you won't have access to do half of the above, in which case you should merely contact your hosting provider and let them investigate this issue for you.

There are plenty of reasons why mail wouldn't reach a give email address.

One of the most common cause of failed mail delivery is due to a given account being overquota. Have you considered this?

To check what is happening, try sending an email to the given email address and then observe the contents of /var/log/exim_mainlog as any error, if the mail is reaching the server, will be recorded here.

Consider also whether the MX record for the domain in question is working correctly. Does it point to the correct IP address, does the IP respond? How busy is the server? Is it overloaded to the extent where received mail is taking a long long long time to process?

Do you have any forwaders or filters in place that could be affecting where mail is delivered? Consider removing them to see what difference this may make.

Lastly, if you're not the server administrator, you won't have access to do half of the above, in which case you should merely contact your hosting provider and let them investigate this issue for you.